Rank one systems are a class of dynamical systems arising in the late 60's and form a rich class of examples and counter-examples in ergodic theory. Notably, the Chacon map was the first known example of a weakly mixing transformation which is not mixing. However, a complete classification of their dynamical properties still remains open. From the topological dynamics viewpoint, we consider symbolic models of rank one systems. In this talk, we will discuss dynamical properties of symbolic rank one subshifts such as mixing, the existence of continuous and measurable eigenvalues, topological factors and the topological rank.